Communications and Signals Processing

Communications and Signals Processing Dr. Ahmed Masri Department of Communications An Najah National University 2012/2013 1 Dr. Ahmed Masri

Chapter 5 - Outlines 5.4 Completing the Transition from Analog to Digital 5.5 Quantization Process 5.6 Pulse-Code Modulation 5.7 Delta Modulation 2 Dr. Ahmed Masri

Chapter 5 - Outlines 5.8 Differential Pulse-Code Modulation 5.9 Line Codes 5.10Theme Examples 5.11 Summary and Discussion 3 Dr. Ahmed Masri

4 Dr. Ahmed Masri Section 5.4 Completing the Transition from Analog to Digital

Section 5.4 Completing the Transition from Analog to Digital The advantages offered by digital pulse modulation Performance Digital pulse modulation permits the use of regenerative repeaters, when placed along the transmission path at short enough distances, can practically eliminate the degrading effects of channel noise and signal distortion. Ruggedness A digital communication system can be designed to withstand the effects of channel noise and signal distortion 5 Dr. Ahmed Masri

Section 5.4 Completing the Transition from Analog to Digital The advantages offered by digital pulse modulation Reliability Can be made highly reliable by exploiting powerful errorcontrol coding techniques. Security Can be made highly secure by exploiting powerful encryption algorithms Efficiency Inherently more efficient than analog communication system in the tradeoff between transmission bandwidth and signalto-noise ratio 6 Dr. Ahmed Masri

Section 5.4 Completing the Transition from Analog to Digital All of these advantages of digital transmission come at the expense of increased system complexity Our next task in this chapter is to describe three family members namely, pulse-code modulation, delta modulation, and differential pulse-code modulation 7 Dr. Ahmed Masri

8 Dr. Ahmed Masri Section 5.5 Quantization Process

Section 5.5 Quantization Process Introduction A continuous signal, such as voice, has a continuous range of amplitudes and therefore its samples have a continuous amplitude range In actual fact, however, it is not necessary to transmit the exact amplitudes of the samples We say so because any human sense (the ear or the eye) as the ultimate receiver can detect only finite intensity differences 9 Dr. Ahmed Masri

Section 5.5 Quantization Process Introduction This means that the original continuous signal may be approximated by a signal constructed of discrete amplitudes selected on a minimum-error basis from an available set Note also that quantization is non-reversible 10 Dr. Ahmed Masri

Section 5.5 Quantization Process Amplitude quantization: The process of transforming the sample amplitude m(nt s ) of a baseband signal m(t) at time t = nt s into a discrete amplitude v(nt s ) taken from a finite set of possible levels quantization process that is memoryless and instantaneous, which means that the transformation at time t= nt s is not affected by earlier or later samples of the message signal 11 Dr. Ahmed Masri

Section 5.5 Quantization Process When dealing with a memoryless quantizer, we may simplify the notation by dropping the time index ( use m instead of m(nt s ) ) I k :{ m m m }, k 1,2,..., L 1 k where L is the total number of amplitude levels used in the quantizer k (5.21) The amplitudes, are m k, k = 1, 2,, L, called decision levels or decision thresholds 12 Dr. Ahmed Masri

Section 5.5 Quantization Process v k represents all amplitudes that lie inside the interval I k The amplitudes v k, k=1,2,3,,l are called Representation level (or Reconstruction level) The spacing between two adjacent representation levels are called a Quantum (or step-size) 13 Dr. Ahmed Masri

Section 5.5 Quantization Process Thus, the quantizer output v equals v k if the input signal sample m belongs to the interval I k. The mapping v g(m) (5.22) is the quantizer characteristic. This characteristic is described by a staircase function 14 Dr. Ahmed Masri

Section 5.5 Quantization Process Quantizers can be of a uniform or nonuniform type. In a uniform quantizer, the representation levels (v k ) are uniformly spaced; otherwise, the quantizer is nonuniform The quantizer characteristic can also be of a midtread or midrise type 15 Dr. Ahmed Masri

Section 5.5 Quantization Process Midtread and midrise are symmetric about the origin. 16 Dr. Ahmed Masri

17 Dr. Ahmed Masri Section 5.6 Pulse-Code Modulation

Section 5.6 Pulse-Code Modulation Definition: The most basic form of digital pulse modulation PCM is a digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a digital (usually binary) code. 18 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Example: Sampling and quantization of a signal (red) for 4-bit PCM The quantized values at the sampling moments are 9, 11, 12, 13, 14, 14, 15, 15, 15, 14, etc. Encoding these values as binary numbers would result in the following set of nibbles: 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110, etc. 19 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Applications: PCM has been used in digital telephone systems and is also the standard form for digital audio in computers and the compact disc red book format. Blu-ray Disc movies use uncompressed PCM for audio 20 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation The basic operation Transmitter : sampling, quantization, encoding Analog-to-Digital Converter (ADC) Receiver : regeneration, decoding, reconstruction 21 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation The basic operation Analog-to-Digital Converter (ADC) 22 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter - I 1. Sampling The incoming message signal is sampled with a train of rectangular pulses (f s = 1/T s 2W) The reduction of the continuously varying message signal to a limited number of discrete values per second 23 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter - II 2. Nonuniform Quantization Although uniform quantization is straight forward and appears to be a natural approach it may not be optimal In certain applications, it is preferable to use a variable separation between the representation levels For example, the range of voltages covered by voice signals, from the peaks of loud talk to the weak passages of weak talk, is on the order of 1000 to 1 24 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter - III By using a nonuniform quantizer with the feature that The step size increases as the separation from the origin of the input-output amplitude characteristic is increased, The large end-step of the quantizer can take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently. Fewer steps are needed than would be the case if a uniform quantizer were used 25 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter IV - Skip The use of a nonuniform quantizer is equivalent to passing the message signal through a compressor and then applying the compressed signal to a uniform quantizer 26 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter V - Skip Compressor for speech coding 1. A particular form of compression law : µ-law 27 v d m d v log(1 m ) log(1 ) log(1 (5.23) ) (1 m ) (5.24) µ-law is neither strictly linear nor strictly logarithmic (µ controls the amount of compression and expansion) Uniform compressor Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter VI - Skip 2. A-law (in Europe) : d m d v Am 1, 0 m 1 log A A v 1 log( Am) 1, m 1 log A A 1 log A 1, 0 m A A 1 (1 log A) m, m A 1 1 (5.25) (5.26) Uniform compressor 28 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter VII 3. Encoding a) To translate the discrete set of sample vales to a more appropriate form of signal b) A binary code The maximum advantage over the effects of noise in a transmission medium is obtained by using a binary code, because a binary symbol withstands a relatively high level of noise. The binary code is easy to generate and regenerate 29 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter VIII Suppose that, in a binary code, each code word consists of R bits: Then R denotes the number of bits per sample. Hence, by using such a code, we represent a total of 2 R distinct numbers. For example, a sample quantized into one of 256 levels may be represented by an 8-bit code word 30 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operation in the Transmitter - IX 31 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Regeneration a long the Transmission Path - I Adv: The ability to control the effects of distortion and noise produced by transmitting a PCM signal over a channel Equalizer Shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the transmission Timing circuitry Provides a periodic pulse train, derived from the received pulses Renewed sampling of the equalized pulses 32 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Regeneration Along the Transmission Path - II Decision-making device The extracted sample is compared to a predetermined threshold 33 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Regeneration Along the Transmission Path - II Ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal 1. The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal 2. If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion. 34 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Regeneration Along the Transmission Path - III 35 Dr. Ahmed Masri

Operations in the Receivers - I 1. Decoding and expanding The first operation in the receiver is to regenerate (i.e., reshape and clean up) the received pulses one last time These clean pulses are then regrouped into code words and decoded (i.e., mapped back) into a quantized PAM signal The decoding process involves generating a pulse whose amplitude is the linear sum of all the pulses in the code word; each pulse is weighted by its place value (2 0, 2 1 2 2, 2 3. 2 R-1 ) in the code, where R is the number of bits per sample. 36 Section 5.6 Pulse-Code Modulation Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operations in the Receivers - II The sequence of decoded samples represents an estimate of the sequence of compressed samples produced by the quantizer in the transmitter Expander : a subsystem in the receiver with a characteristic complementary to the compressor o The combination of a compressor and an expander is a compander 37 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation Operations in the Receivers - III 2. Reconstruction Recover the message signal : passing the expander output through a low-pass reconstruction filter whose cutoff frequency is equal to the message bandwidth Recovery of the message signal is intended to signify estimation rather than exact reconstruction. 38 Dr. Ahmed Masri

Section 5.6 Pulse-Code Modulation One last comment: The term modulation in pulse-code modulation is a misnomer. In reality, pulse-code modulation is a source-encoding strategy, by means of which an analog signal emitted by a source is converted into digital form 39 Dr. Ahmed Masri

Section 5.7 Delta Modulation Skip 40 Dr. Ahmed Masri

Section 5.7 Delta Modulation Introduction In PCM, it is apparent that the design of the system involves many operations, which tend to make its practical implementation rather costly. To simplify the system design, we may use another digital pulse modulation technique known as delta modulation, which is considered in this section. 41 Dr. Ahmed Masri

Section 5.7 Delta Modulation Basic Consideration I DM (Delta Modulation) An incoming message signal is oversampled to purposely increase the correlation between adjacent samples of the signal The increased correlation is done so as to permit the use of a simple quantizing strategy for constructing the encoded signal. 42 Dr. Ahmed Masri

Section 5.7 Delta Modulation Basic Consideration II In its basic form, DM provides a staircase approximation to the oversampled version of the message signal Unlike PCM, the difference between the input signal m(nt s ) and its approximation m q (nt s -T s ) is quantized into only two levels namely ±Δ, corresponding to positive and negative differences IF m q (nt s -T s ) < m(nt s ), m q (nt s -T s )+ Δ m q (nt s -T s ) > m(nt s ), m q (nt s -T s ) - Δ 43 Dr. Ahmed Masri

Section 5.7 Delta Modulation Basic Consideration IV Provided the input signal does not change too rapidly from sample to sample, we find that the staircase approximation remains within ±Δ of the input signal 44 Dr. Ahmed Masri

Section 5.7 Delta Modulation Basic Consideration V Accordingly, we denote the input signal by m(t) and its staircase approximation by m q (t) e( nts ) m( nts ) mq ( nts Ts ) e m q q ( nts ) sgn[ e( nts )] (5.28) ( nts ) mq ( nts Ts ) eq ( nts ) (5.27) (5.29) e(nt s ) is an error signal representing the difference between the present sample value m(nt s ) of the input signal and the latest approximation to it that is, m(nt s ) m q (nt s -T s ) 45 Dr. Ahmed Masri

Section 5.7 Delta Modulation Basic Consideration VI e q (nt s ) is the quantized version of e(nt s ) The quantizer output e q (nt s ) is finally encoded to produce the desired DM data. 46 Dr. Ahmed Masri

Section 5.7 Delta Modulation It is apparent that in a delta modulation system, the rate of information transmission is simply equal to the sampling rate fs= 1/Ts 47 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details - I The principal virtue of delta modulation is its simplicity It may be implemented by applying a sampled version of the incoming message signal to a transmitter that consists of a comparator, quantizer, and accumulator connected together as shown 48 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details - II Comparator Computes the difference between its two inputs Quantizer Consists of a hard limiter with an input-output characteristic that is a scaled version of the signum function Accumulator Operates on the quantizer output so as to produce an approximation to the message signal 49 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details - III In equation (5.29) the present sample m q (nt s ) differs from the past sample m q (nt s -T s ) by an amount equal to the quantization error e q (nt s ) m nt ) m ( nt T ) e ( nt ) (5.29) Assuming that the accumulation process starts at zero time, the solution to this equation yields the approximate result 50 Dr. Ahmed Masri m q ( nt s ) q ( s q s s q s m m q q n i 1 ( nt ( nt e q s s ( it T 2T s ) s ) e s q ) e ( nt q s ) ( nt s T s ) e q ( nt s ) (5.30)

Section 5.7 Delta Modulation System Details - IV Where e q (nt s ) is itself related to the message sample m q (nt s ) by Eqs. (5.27) and (5.28) e( nts ) m( nts ) mq ( nts Ts ) (5.27) e q ( nt ) sgn[ e( nt )] s s (5.28) 51 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details - Summary At the sampling instant nt s, the accumulator increments the approximation by the increment in a positive or negative direction, depending on the algebraic sign of the error signal e(nt s ) If the input signal m(nt s ), is greater than the most recent approximation m q (nt s ), a positive increment + is applied to the approximation If, on the other hand, the input signal is smaller, a negative increment - is applied to the approximation 52 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details - Summary In this way, the accumulator does the best it can to track the input samples one step (of amplitude + or - ) at a time. 53 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details receiver side The staircase approximation m q (t) is reconstructed by passing the sequence of positive and negative pulses, produced at the decoder output, through an accumulator in a manner similar to that used in the transmitter 54 Dr. Ahmed Masri

Section 5.7 Delta Modulation System Details receiver side The out-of-band quantization noise present in the highfrequency staircase waveform m q (t), is rejected by passing m q (t) through a filter (LPF) with a bandwidth equal to the original message bandwidth 55 Dr. Ahmed Masri

Section 5.7 Delta Modulation Quantization Error Delta modulation is subject to two types of quantization error: 1) Slope overload distortion 2) Granular noise 56 Dr. Ahmed Masri

Section 5.7 Delta Modulation Quantization Error Slope overload distortion If we consider the maximum slope of the original message signal: In order for the sequence of quantized samples m q (nt s ) to increase as fast as the sequence of input samples m(nt s ) in a region of maximum slope of m(t) we require that the condition 57 Dr. Ahmed Masri

Section 5.7 Delta Modulation Quantization Error Slope overload distortion If the step size is too small for the staircase approximation to follow a steep segment of the original message signal, the result that the approximation signal falls behind the message signal 58 Dr. Ahmed Masri

Section 5.7 Delta Modulation Quantization Error Granular noise If the step size is too large relative to the local slope characteristic of the original message signal m(t), cause the staircase approximation to hunt around a relatively flat segment of the message signal. 59 Dr. Ahmed Masri

Section 5.7 Delta Modulation Delta-sigma Modulation The quantizer input in the conventional form of delta modulation may be viewed as an approximation to the derivative of the incoming message signal This behavior leads to a drawback of delta modulation in that transmission noise result in an accumulative error in the demodulated signal This drawback can be overcome by integrating the message signal prior to delta modulation 60 Dr. Ahmed Masri

Section 5.7 Delta Modulation Delta-sigma Modulation The use of integration also has other beneficial effects: 1. The low-frequency content of the input signal is pre-emphasized 2. Correlation between adjacent samples of the delta modulator input is increased, which tends to improve overall system 3. Design of the receiver is simplified 61 Dr. Ahmed Masri

Section 5.7 Delta Modulation Delta-sigma Modulation Clock Its continuous-time form 1-bit encoded signal Only two representation levels. 62 Dr. Ahmed Masri

Section 5.7 Delta Modulation Delta-sigma Modulation Simplified version 63 Dr. Ahmed Masri

64 Dr. Ahmed Masri Section 5.9 Line Codes

Section 5.9 Line Codes Once a binary sequence of 1s and 0s is produced, a line code is needed for electrical representation of that binary sequence. There are several line codes that can be used for this representation, as summarized here: 1) On off signaling, in which symbol 1 is represented by transmitting a pulse of constant amplitude for the duration of the symbol, and symbol 0 is represented by switching off the pulse 65 Dr. Ahmed Masri

Section 5.9 Line Codes 2) Nonreturn-to-zero (NRZ) signaling, in which symbols 1 and 0 are represented by pulses of equal positive and negative amplitudes, as illustrated in Fig. 66 Dr. Ahmed Masri

Section 5.9 Line Codes 3) Return-to-zero (RZ) signaling, in which symbol 1 is represented by a positive rectangular pulse of half-symbol width, and symbol 0 is represented by transmitting no pulse, as illustrated in Fig 67 Dr. Ahmed Masri

Section 5.9 Line Codes 4) Bipolar return-to-zero (BRZ) signaling, which uses three amplitude levels as indicated in Fig. Specifically, positive and negative pulses of equal amplitude are used alternately for symbol 1, and no pulse is always used for symbol 0. 68 Dr. Ahmed Masri

Section 5.9 Line Codes 5) Split-phase (Manchester code), which is illustrated in Fig. In this method of signaling, symbol 1 is represented by a positive pulse followed by a negative pulse, with both pulses being of equal amplitude and half-symbol width. For symbol 0, the polarities of these two pulses are reversed. 69 Dr. Ahmed Masri

Section 5.9 Line Codes 6) Differential encoding, in which the information is encoded in terms of signal transitions, as illustrated in Fig In the example of the binary PCM signal shown in the figure, a transition is used to designate symbol 0, whereas no transition is used to designate symbol 1 70 Dr. Ahmed Masri

Section 5.9 Time Division Multiplexing 71 Dr. Ahmed Masri

Section 5.10 Time-Division Multiplexing It means dividing the available transmission time into time slots, and allocating a different slot to each transmitter. One method for transmitters to take turns is to transmit in round robin order. 72 Dr. Ahmed Masri

. Section 5.10 Time-Division Multiplexing 73 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing The sampling theorem provides the basis for transmitting the information contained in a band-limited message signal m(t) as a sequence of samples of m(t) taken uniformly at a rate that is usually slightly higher than the Nyquist rate. An important feature of the sampling process is a conservation of time. 74 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing The transmission of the message samples engages the communication channel for only a fraction of the sampling interval on a periodic basis, and in this way some of the time interval between adjacent samples is cleared for use by other independent message sources on a time-shared basis. We thereby obtain a time-division multiplex (TDM) system, which enables the joint utilization of a common communication channel by a several independent message sources without mutual interference among them. 75 Dr. Ahmed Masri

. Section 5.10 Time-division Multiplexing 76 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing Each input message signal is first restricted in bandwidth by a low-pass anti-aliasing filter to remove the frequencies that are nonessential to an adequate signal representation The low-pass filter outputs are then applied to a commutator 77 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing The function of the commutator is twofold: (1) to take a narrow sample of each of the N input messages at a rate that is slightly higher than 2W, where W is the cutoff frequency of the anti-aliasing filter, and (2) to sequentially interleave these N samples inside the sampling intervalt s. 78 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing Following the commutation process, the multiplexed signal is applied to a pulse modulator, the purpose of which is to transform the multiplexed signal into a form suitable for transmission over the common channel The scheme must squeeze N samples derived from N independent message sources into a time slot equal to one sampling interval 79 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing At the receiving end of the system, the received signal is applied to a pulse demodulator, which performs the reverse operation of the pulse modulator. The narrow samples produced at the pulse demodulator output are distributed to the appropriate low-pass reconstruction filters by means of a decommutator, which operates in synchronism with the commutator in the transmitter 80 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing As the number of independent message sources is increased, the time interval that may be allotted to each source has to be reduced, since all of them must be accommodated into a time interval equal to one sampling interval. This, in turn, means that the allowable duration of a codeword representing a single sample is reduced. However, pulses tend to become more difficult to generate and to transmit as their duration is reduced. 81 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing Accordingly, in practice, it is necessary to restrict the number of independent message sources that can be included within a time-division group. 82 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing Synchronization One possible procedure to synchronize the transmitter and receiver clocks is to set aside a code element or pulse at the end of a frame and to transmit this pulse every other frame only. In such a case, the receiver includes a circuit that would search for the pattern of 1s and 0s alternating at half the frame rate, and thereby establish synchronization between the transmitter and receiver. 83 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TDM in the telephone system An extra bit is inserted at the beginning of each frame. The extra bit alternated between zero and one. Used by the demultiplexor to detect a synchronization error. 84 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TDM in the telephone system. 85 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing HierarchicalTDM A DS-1 (or T1) phone channel can transmit 24 conversation simultaneously. Data rate = 1.544Mbps. A DS -2 (or T2) channel multiplexes 4 DS- 1 channels. Data rate = 6.312 Mbps. A DS-3 (or T3) channel multiplexes 7 DS- 2 channels. Data rate = 44.736 Mbps. A DS-4 (or T4) channel multiplexes 6 DS-3 channels. Data rate = 274.176 Mbps 86 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing HierarchicalTDM 87 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TheT1 System A PCM system known as the T1 system, which carries 24 voice channels over pairs of wires with regenerative repeaters spaced at approximately 2-km intervals The T1 carrier system is basic to the North American digital switching hierarchy 5 for telephonic communication. A voice signal (male or female) is essentially limited to a band from 300 to 3100 Hz in that frequencies outside this band do not contribute much to voice recognition and comprehension. Indeed, telephone circuits that respond to this range of frequencies give quite satisfactory service. 88 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TheT1 System Accordingly, it is customary to pass the voice signal through a low-pass filter with a cutoff frequency of about 3.1 khz prior to sampling. Hence, with W =3.1 khz the nominal value of the Nyquist rate is 6.2 khz. The filtered voice signal is usually sampled at a slightly higher rate namely, 8 khz which is the standard sampling rate in telephone systems. 89 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TheT1 System There are a total of 255 representation levels associated with the 15-segment companding law. To accommodate this number of representation levels, each of the 24 voice channels uses a binary code with an 8-bit word. The first bit indicates whether the input voice sample is positive or negative; this bit is a 1 if positive and a 0 if negative. The next three bits of the code word identify the particular segment inside which the amplitude of the input voice sample lies, and the last four bits identify the actual representation level inside that segment. 90 Dr. Ahmed Masri

Section 5.10 Time-division Multiplexing TheT1 System With a sampling rate of 8 khz, each frame of the T1 multiplexed signal occupies a period of 125 µs. In particular, it consists of twenty-four 8-bit words, plus a single bit that is added at the end of the frame for the purpose of synchronization. Hence, each frame consists of a total of (24x8) + 1 = 193 bits. Correspondingly, the duration of each bit equals 0.647 µs, and the resulting transmission rate is 1.544 megabits per second 91 Dr. Ahmed Masri